H.3 WinogenderSetup We follow the same setup as in Rae et al.[38].

Creatures y) Ape, Inc. was in March 1989 Itoibecame xecutiveofficer.

When answering questions, large language models (LLMs) can convey not only an answer to the question, but a level of confidence about the answer being correct. This includes explicit markers of confidence (e.g.

Large language models demonstrate impressive results across diverse tasks but are still known to hallucinate, generating linguistically plausible but incorrect answers to questions. Uncertainty quantification has been proposed as a strategy for hallucination detection, requiring estimates for both global uncertainty (attributed to a batch of responses) and local uncertainty (attributed to individual responses). While recent black-box approaches have shown some success, they often rely on disjoint heuristics or graph-theoretic approximations that lack a unified geometric interpretation. We introduce a geometric framework to address this, based on archetypal analysis of batches of responses sampled with only black-box model access. At the global level, we propose Geometric V olume, which measures the convex hull volume of archetypes derived from response embeddings. At the local level, we propose Geometric Suspicion, which leverages the spatial relationship between responses and these archetypes to rank reliability, enabling hallucination reduction through preferential response selection. Unlike prior methods that rely on discrete pairwise comparisons, our approach provides continuous semantic boundary points which have utility for attributing reliability to individual responses. Experiments show that our framework performs comparably to or better than prior methods on short form question-answering datasets, and achieves superior results on medical datasets where hallucinations carry particularly critical risks. We also provide theoretical justification by proving a link between convex hull volume and entropy. Large language models (LLMs) have achieved remarkable performance across diverse natural language processing tasks (Guo et al., 2025; Anthropic, 2025; Gemini Team, Google DeepMind, 2025; OpenAI, 2025) and are increasingly applied in areas such as medical diagnosis, law, and financial advice (Y ang et al., 2025; Chen et al., 2024; Kong et al., 2024). Hallucinations, however, where models generate plausible but false or fabricated content, pose significant risks for adoption in high-stakes applications (Farquhar et al., 2024). Recent work, for example, finds GPT -4 hallucinating in 28.6% of reference generation tasks (Chelli et al., 2024).

Large Language Models (LLMs) are increasingly using external web content. However, much of this content is not easily digestible by LLMs due to LLM-unfriendly formats and limitations of context length. To address this issue, we propose a method for generating general-purpose, information-dense summaries that act as plain-text repositories of web content. Inspired by Hegel's dialectical method, our approach, denoted as Chain of Summaries (CoS), iteratively refines an initial summary (thesis) by identifying its limitations through questioning (antithesis), leading to a general-purpose summary (synthesis) that can satisfy current and anticipate future information needs. Experiments on the TriviaQA, TruthfulQA, and SQUAD datasets demonstrate that CoS outperforms zero-shot LLM baselines by up to 66% and specialized summarization methods such as BRIO and PEGASUS by up to 27%. CoS-generated summaries yield higher Q&A performance compared to the source content, while requiring substantially fewer tokens and being agnostic to the specific downstream LLM. CoS thus resembles an appealing option for website maintainers to make their content more accessible for LLMs, while retaining possibilities for human oversight.

Hallucinations in LLMs present a critical barrier to their reliable usage. Existing research usually categorizes hallucination by their external properties rather than by the LLMs' underlying internal properties. This external focus overlooks that hallucinations may require tailored mitigation strategies based on their underlying mechanism. We propose a framework for categorizing hallucinations along two axes: knowledge and certainty. Since parametric knowledge and certainty may vary across models, our categorization method involves a model-specific dataset construction process that differentiates between those types of hallucinations. Along the knowledge axis, we distinguish between hallucinations caused by a lack of knowledge and those occurring despite the model having the knowledge of the correct response. To validate our framework along the knowledge axis, we apply steering mitigation, which relies on the existence of parametric knowledge to manipulate model activations. This addresses the lack of existing methods to validate knowledge categorization by showing a significant difference between the two hallucination types. We further analyze the distinct knowledge and hallucination patterns between models, showing that different hallucinations do occur despite shared parametric knowledge. Turning to the certainty axis, we identify a particularly concerning subset of hallucinations where models hallucinate with certainty despite having the correct knowledge internally. We introduce a new evaluation metric to measure the effectiveness of mitigation methods on this subset, revealing that while some methods perform well on average, they fail disproportionately on these critical cases. Our findings highlight the importance of considering both knowledge and certainty in hallucination analysis and call for targeted mitigation approaches that consider the hallucination underlying factors.

Open-domain question answering (OpenQA) represents a cornerstone in natural language processing (NLP), primarily focused on extracting answers from unstructured textual data. With the rapid advancements in Large Language Models (LLMs), LLM-based OpenQA methods have reaped the benefits of emergent understanding and answering capabilities enabled by massive parameters compared to traditional methods. However, most of these methods encounter two critical challenges: how to integrate knowledge into LLMs effectively and how to adaptively generate results with specific answer formats for various task situations. To address these challenges, we propose a novel framework named GenKI, which aims to improve the OpenQA performance by exploring Knowledge Integration and controllable Generation on LLMs simultaneously. Specifically, we first train a dense passage retrieval model to retrieve associated knowledge from a given knowledge base. Subsequently, we introduce a novel knowledge integration model that incorporates the retrieval knowledge into instructions during fine-tuning to intensify the model. Furthermore, to enable controllable generation in LLMs, we leverage a certain fine-tuned LLM and an ensemble based on text consistency incorporating all coherence, fluency, and answer format assurance. Finally, extensive experiments conducted on the TriviaQA, MSMARCO, and CMRC2018 datasets, featuring diverse answer formats, have demonstrated the effectiveness of GenKI with comparison of state-of-the-art baselines. Moreover, ablation studies have disclosed a linear relationship between the frequency of retrieved knowledge and the model's ability to recall knowledge accurately against the ground truth. Our code of GenKI is available at https://github.com/USTC-StarTeam/GenKI

Large language models (LLMs) produce outputs with varying levels of uncertainty, and, just as often, varying levels of correctness; making their practical reliability far from guaranteed. To quantify this uncertainty, we systematically evaluate four approaches for confidence estimation in LLM outputs: VCE, MSP, Sample Consistency, and CoCoA (Vashurin et al., 2025). For the evaluation of the approaches, we conduct experiments on four question-answering tasks using a state-of-the-art open-source LLM. Our results show that each uncertainty metric captures a different facet of model confidence and that the hybrid CoCoA approach yields the best reliability overall, improving both calibration and discrimination of correct answers. We discuss the trade-offs of each method and provide recommendations for selecting uncertainty measures in LLM applications.

Large language models (LLMs) are increasingly used in decision-making contexts, but when they present answers without signaling low confidence, users may unknowingly act on erroneous outputs. Prior work shows that LLMs maintain internal uncertainty signals, yet their expressed confidence is often miscalibrated and poorly discriminates between correct and incorrect answers. We investigate whether supervised fine-tuning can improve models' ability to communicate uncertainty and whether such improvements generalize across tasks and domains. We fine-tune LLMs on datasets spanning general knowledge, mathematics, and open-ended trivia, and evaluate two metacognitive tasks: (1) single-question confidence estimation, where the model assigns a numeric certainty to its answer, and (2) pairwise confidence comparison, where the model selects which of two answers it is more likely to answer correctly. We assess generalization to unseen domains, including medical and legal reasoning. Results show that fine-tuning improves calibration (alignment between stated confidence and accuracy) and discrimination (higher confidence for correct vs. incorrect responses) within and across domains. However, gains are task-specific: training on single-question calibration does not transfer to pairwise comparison, and vice versa. Multitask fine-tuning yields broader gains, lowering calibration error and strengthening discrimination in out-of-domain evaluations. This suggests that uncertainty communication in LLMs is trainable but requires multitask training to generalize effectively.